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Εργοδική Θεωρία
Εργοδική Θεωρία Ergodic Theory, List of quantum field theories thumb|300px| [[Επιστήμη Επιστήμες Φυσικές Επιστήμες Βιο-Επιστήμες Γεω-Επιστήμες Οικονομικές Επιστήμες Θεωρητικές Επιστήμες Κοινωνικές Επιστήμες Επιστήμες Υγείας ---- Τεχνολογία ---- Επιστημονικός Κλάδος Επιστημονικός Νόμος Επιστημονική Μέθοδος Επιστημονική Θεωρία Επιστημονικά Κέντρα Γης Επιστήμονες Γης ]] thumb|300px| [[Επιστημονική Θεωρία Ιδιότητες ---- [[Αναγνωρισιμότητα |Αναγνωρισιμότητα (Identifiability)]] [[Επαληθευσιμότητα |Επαληθευσιμότητα (Verifiability)]] [[Ελεγξιμότητα |Ελεγξιμότητα (Testability)]] [[Προβλεψιμότητα|Προβλεψιμότητα (Predictivity)]] [[Αυτοσυνέπεια|Αυτοσυνέπεια (Self-consistency)]] [[Συμβατότητα|Συμβατότητα (Compatibility)]] [[Συνεκτικότητα|Συνεκτικότητα (Connectivity)]] [[Συμπαγότητα|Συμπαγότητα (Compactibility)]] [[Οικονομικότητα|Οικονομικότητα (Thriftiness)]] [[Επαγωγικότητα|Επαγωγικότητα (Inductivity)]] [[Αναγωγισιμότητα|Αναγωγισιμότητα (Reducibility)]] [[Συμπτυξιμότητα|Συμπτυξιμότητα (Shortenability)]] ]] thumb|300px| [[Επιστημονική Θεωρία ]] - Μια Φυσική Θεωρία. Ετυμολογία Η ονομασία "πεδιακή" σχετίζεται ετυμολογικά με την λέξη "Πεδίο". Εισαγωγή Ergodic theory (Ancient Greek: ergon work, hodos way) is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed to run for a long time. The first result in this direction is the Poincare recurrence theorem, which claims that almost all points in any subset of the phase space eventually revisit the set. More precise information is provided by various ergodic theorems which assert that, under certain conditions, the time average of a function along the trajectories exists almost everywhere and is related to the space average. Two of the most important theorems are those of George David Birkhoff (1931) and John von Neumann which assert the existence of a time average along each trajectory. For the special class of ergodic systems, this time average is the same for almost all initial points: statistically speaking, the system that evolves for a long time "forgets" its initial state. Stronger properties, such as mixing and equidistribution, have also been extensively studied. The problem of metric classification of systems is another important part of the abstract ergodic theory. An outstanding role in ergodic theory and its applications to stochastic processes is played by the various notions of measure-theoretic entropy for dynamical systems. The concepts of ergodicity and the ergodic hypothesis are central to applications of ergodic theory. The underlying idea is that for certain systems the time average of their properties is equal to the average over the entire space. Applications of ergodic theory to other parts of mathematics usually involve establishing ergodicity properties for systems of special kind. In geometry, methods of ergodic theory have been used to study the geodesic flow on Riemannian manifolds, starting with the results of Eberhard Hopf for Riemann surfaces of negative curvature. Markov chains form a common context for applications in probability theory. Ergodic theory has fruitful connections with harmonic analysis, Lie theory (representation theory, lattices in algebraic groups), and number theory (the theory of diophantine approximations, L-functions). Υποσημειώσεις Εσωτερική Αρθρογραφία *Φυσικό Πεδίο *Φυσική Θεωρία *Κλασσική Πεδιακή Θεωρία *Σχετικιστική Πεδιακή Θεωρία *Κβαντική Πεδιακή Θεωρία *Τοπολογική Πεδιακή Θεωρία (Topological field theory ) *Σύμμορφη Πεδιακή Θεωρία (conformal field theory) * Κρυσταλλική Πεδιακή Θεωρία (Crystal field theory) * Effective field theory * Unified field theory * Mean field theory * Gauge field theory * Ligand field theory * Psychological field theory * Sociological field theory *Class field theory *String field theory *Statistical field theory *Local class field theory *Covariant Hamiltonian field theory *Thermal quantum field theory *Toda field theory *Local quantum field theory *Lattice field theory *Liouville field theory *Noncommutative quantum field theory *Phenomenal field theory *Polymer field theory *Qubit field theory *Decision field theory *Lexical field theory *Dynamical mean field theory *Algebraic quantum field theory *Constructive quantum field theory *Rational conformal field theory *Irrational conformal field theory *Logarithmic conformal field theory *Boundary conformal field theory Βιβλιογραφία * * Ιστογραφία *Ομώνυμο άρθρο στην Βικιπαίδεια *Ομώνυμο άρθρο στην Livepedia *[ ] *[ ] Κατηγορία:Φυσικές Θεωρίες